In the movie Terminator Genisys, they show that the series of events from the first terminator never happens. This is an alternate timeline. They also destroy subsequent chips from other terminators. How does Skynet get built then? Isn't the existence of Skynet based on the result of the Predestination paradox? If they didn't have the machine chip, by who and how does Skynet get created?
They got help from someone
John Connor / T-3000
This guy is from future and he might have brought a skynet chip with him else helped creating a one with the name Genisys. As skynet himself sent him in past, so he must have secured his existence too.